For the first time an analytic expression was obtained for the inelastic neutron scattering law with an isotropic neutron source within the gas model, considering moderating medium temperature as a parameter. The inelastic scattering law is obtained, based on the solution of the kinematic problem of neutron inelastic scattering on a nucleus in laboratory coordinate system (L-system) in general case. I.e. in case not only a neutron but also a nucleus have arbitrary velocity vector in L-system. Analytic expressions are found for the neutron flux density and moderation spectrum in reactor fissile medium, both in case of the elastic scattering law, obtained earlier by the authors, and in case of the inelastic scattering law obtained in this paper. Both elastic and inelastic scattering laws are considered to be dependent on the medium temperature. The obtained expressions for neutron moderation spectra enable reinterpretation of physical nature of the processes that determine the shape of neutron spectrum in a wide energy range.
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